Questions tagged [linear-algebra]
For questions related to linear mappings, matrices, basis, determinants, eigenvalues and other topics commonly done in a linear algebra course.
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Questions about writing a Linear Algebra textbook, with Earth Science applications
I am writing a Linear Algebra textbook that is supposed to have several Earth Science applications (Geophysics, Atmospheric Science) given that I come from an Earth/Atmospheric Science background. I ...
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2
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Producing defective matrix examples
It's easy to come up with examples of interesting diagonalizable matrices $A\in M_n(\mathbb{C})$ with a prescribed set of eigenvalues $\lambda_1,\dots,\lambda_n$ because you can start with your ...
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What Basic Math Skills Should Be Expected of Students in a University-Level Linear Algebra Course?
I am currently teaching a university-level linear algebra course and recently encountered an issue that made me question the assumed foundational math skills for students in this course. The issue ...
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3
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Regarding finding eigenvalues and minimal polynomial of an operator with limited tools while following Sheldon Axler
I am using the textbook Linear Algebra done right by Sheldon Axler (fourth edition) to teach an undergraduate linear algebra course.
Please find here a link to the book here.
Now Axler does not ...
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1
answer
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Condense a logistic function around its midpoint [closed]
I have a function
$$
f(x) = {1 \over 1 + e^{-k(x-0.5)}}
$$
that plots a logistic curve that is symmetric around the point $0.5 / 0.5$.
$k$ defines the steepness of the curve.
I would now like to add ...
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1
answer
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Help finding a YouTube channel for Linear Algebra
I remember watching a youtube playlist on a video about equation of a plane and about vectors in 3D. The video was fully animated in 3D and had good sound effects too. I feel like it had a clock ...
6
votes
3
answers
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Game project using linear algebra
Throughout this year, I have been in charge of a linear algebra course aimed at engineering school. In this course, I asked my students to work on a final project involving finding a winning strategy ...
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What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?
I have helped to TA and taught several courses with mixtures of advanced undergraduate and early graduate students in engineering/STEM. These courses are the classics: signal processing, control, ...
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4
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3
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Looking for web app resources for symbolic Gaussian elimination
I am looking for a web app software that takes step-by-step directions from a student to perform the linear combination operation on a matrix with symbolic coefficients (as opposed to just numbers). ...
- 1,410
0
votes
2
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How to intuitively connect Linear Equation in two variables and the graph of them? [closed]
I struggle with connecting graphs of linear equation with algebraic form like $x+y=p$.
How do I develop the intuition that it represents a line that is sloping down and passes through value $p$ on $y$-...
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What is the dimension of $\mathbb{R}$ over $\mathbb{Q}$?
Long time ago a student asked me what the dimension of $\mathbb{R}$ over $\mathbb{Q}$ is, and I said
$$\dim_{\mathbb{Q}}\mathbb{R}=\mathfrak{c}$$
where $\mathfrak{c}$ is the cardinality of the ...
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4
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2
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Programming and computation-focused textbook for introductory linear algebra
tl;dr I am looking for references which cover introductory abstract Linear Algebra but with a programming / computational approach. The only one I found is the Jupyter guide to Linear Algebra
Long ...
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Why do we teach linear algebra in precalculus classes?
When I took precalculus, we learned about polynomials and how to factor them, we learned about trigonometry and lots of great and useful identities there, and we learned about matrices. They didn't ...
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1
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Rediscovering euqation of line [closed]
I am studying (self learner) linear equations/equation of line and my idea is to discover the equations myself rather than try and understand ready-made equations available in text books. I am using X-...
- 345
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Lowercase vs. uppercase letters for matrix entries
For a matrix $A$ in, say for instance, $\mathbb{R}^{m \times n}$, there are at least two different conventions to denote its entry at position $(j,k)$:
Denote the entry as $a_{jk}$.
Denote the entry ...
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